题目内容
（本题满分9分）如图所示，△ABC内接于⊙O，AB是⊙O的直径，点D在⊙O
上，过点C的切线交AD的延长线于点E，且AE⊥CE，连接CD．
（1）求证：DC=BC；
（2）若AB=5，AC=4，求tan∠DCE的值．
（1）证明：连接OC················································································· 1分
∵OA＝OC
∴∠OAC＝∠OCA
∵CE是⊙O的切线
∴∠OCE＝90° ·············································· 2分
∵AE⊥CE
∴∠AEC＝∠OCE＝90°
∴OC∥AE ·················································· 3分
∴∠OCA＝∠CAD ∴∠CAD＝∠BAC
∴
∴DC＝BC ··························································································· 4分
（2）∵AB是⊙O的直径 ∴∠ACB＝90°
∴·························································· 5分
∵∠CAE＝∠BAC ∠AEC＝∠ACB＝90°
∴△ACE∽△ABC······················································································ 6分
∴ ∴
······················································ 7分
∵DC＝BC＝3
∴····················································· 8分
∴-----------9分 (其它解法参考得分)
解析:略
.（本题满分5分）如图一根木棒放在数轴上，木棒的左端与数轴上的点A重合，右端与点B重合．
 |
1.若将木棒沿数轴向右水平移动，则当它的左端移动到B点时，它的右端在数轴上所对应的数为20；若将木棒沿数轴向左水平移动，则当它的右端移动到A点时，则它的左端在数轴上所对应的数为5（单位：cm），由此可得到木棒长为 cm．
2.由题(1)的启发,请你借助“数轴”这个工具帮助小红解决下列问题:
问题:一天，小红去问曾当过数学老师现在退休在家的爷爷的年龄，爷爷说：“我若是你现在这么大，你还要40年才出生；你若是我现在这么大，我已经125岁，是老寿星了，哈哈！”，请求出爷爷现在多少岁了？
．
中，点
是
的中点，连接
并延长，交
的延长线于点F．
．
交
轴于
两点，交
轴于点
.
（2）若此抛物线的对称轴与直线
交于点D，作⊙D与x轴相切，⊙D交